As shown in FIG. 1, to carry out soft-decision decoding of an error-correcting code such as a Low-Density Parity-Check (LDPC) code and turbo code from the symbol coordinates of received signal points a receiver of a communication system receives, an LLR computation device 100 calculates LLRs representing the reliability of transmission bits, and supplies the calculated bit LLRs to a soft-decision error correction decoder 110 that performs the error correction decoding and calculates an estimated bit string.
When a modulation scheme the communication system employs is a multivalued modulation scheme such as Phase Shift Keying (PSK), Amplitude Phase Shift Keying (APSK) and Quadrature amplitude modulation (QAM), each transmission symbol point comprises a plurality of bits. Designating the bit LLR of a kth bit among them by Lk, Lk is calculated by the following Expression (1).
                              L          k                =                              ln            ⁢                                          ∑                                                      s                    i                                    ∈                                      C                                          k                      ,                      0                                                                                  ⁢                              exp                ⁡                                  (                                      -                                                                                                                                                  r                            -                                                          s                              i                                                                                                                                2                                                                    2                        ⁢                                                  σ                          2                                                                                                      )                                                              -                      ln            ⁢                                          ∑                                                      s                    i                                    ∈                                      C                                          k                      ,                      1                                                                                  ⁢                              exp                ⁡                                  (                                      -                                                                                                                                                  r                            -                                                          s                              i                                                                                                                                2                                                                    2                        ⁢                                                  σ                          2                                                                                                      )                                                                                        (        1        )            
In Expression (1), r is the located vector (I coordinate, Q coordinate) of the received signal point, si is the located vector of a transmission symbol point, Ck, 0 is a set of all the transmission symbol points with the kth bit being 0, Ck, 1 is a set of all the transmission symbol points with the kth bit being 1, and σ is the standard deviation of Gaussian noise of a communication channel.
To calculate the bit LLR by Expression (1), it is necessary to calculate exponential functions exps, followed by adding the calculation results, and to calculate a logarithmic function ln of the sum, which results in enormous amount of computations. To implement the computations with a circuit is not practical from the viewpoint of a circuit scale.
In view of this, Non-Patent Document 1, for example, shows an approximation technique that leaves only a maximum value in the exps to be added in Expression (1) and neglects the others. Expression (2) shows the approximation method in the equation. In Expression (2), sk, 0, min is the located vector of a point closest to the received signal point r in the transmission symbol points with their kth bit being 0, and sk, 1, min is the vector of the point closest to the received signal point r in the transmission symbol points with their kth bit being 1.
                                                                        L                k                            =                            ⁢                                                ln                  ⁢                                                            ∑                                                                        s                          i                                                ∈                                                  C                                                      k                            ,                            0                                                                                                                ⁢                                          exp                      ⁡                                              (                                                  -                                                                                                                                                                                      r                                  -                                                                      s                                    i                                                                                                                                                              2                                                                                      2                              ⁢                                                              σ                                2                                                                                                                                    )                                                                                            -                                                                                                      ⁢                              ln                ⁢                                                      ∑                                                                  s                        i                                            ∈                                              C                                                  k                          ,                          1                                                                                                      ⁢                                      exp                    ⁡                                          (                                              -                                                                                                                                                                          r                                -                                                                  s                                  i                                                                                                                                                    2                                                                                2                            ⁢                                                          σ                              2                                                                                                                          )                                                                                                                                              ≈                            ⁢                                                ln                  ⁢                                                                          ⁢                                                            max                                                                        s                          i                                                ∈                                                  C                                                      k                            ,                            0                                                                                                                ⁢                                          exp                      ⁡                                              (                                                  -                                                                                                                                                                                      r                                  -                                                                      s                                    i                                                                                                                                                              2                                                                                      2                              ⁢                                                              σ                                2                                                                                                                                    )                                                                                            -                                                                                                      ⁢                              ln                ⁢                                                                  ⁢                                                      max                                                                  s                        i                                            ∈                                              C                                                  k                          ,                          1                                                                                                      ⁢                                      exp                    ⁡                                          (                                              -                                                                                                                                                                          r                                -                                                                  s                                  i                                                                                                                                                    2                                                                                2                            ⁢                                                          σ                              2                                                                                                                          )                                                                                                                                              =                            ⁢                                                                                          -                                                                                                                              r                            -                                                          s                                                              k                                ,                                0                                ,                                                                                                                                  ⁢                                min                                                                                                                                                              2                                                              +                                                                                                                    r                          -                                                      s                                                          k                              ,                              1                              ,                                                                                                                          ⁢                              min                                                                                                                                                  2                                                                            2                    ⁢                                          σ                      2                                                                      :=                                  L                                      1                    ,                    k                                                                                                          (        2        )            
The LLR computation technique according to Expression (2) of the Non-Patent Document 1 will be described using an example of 256 QAM, one of the multivalued modulation schemes, with reference to a drawing. As shown in FIG. 2, the 256 QAM is a multivalued modulation scheme which has symbols each consisting of 8 bits a1 a2 a3 . . . a8, and has 256 transmission symbol points. The LLR computation technique according to Expression (2) calculates transmission symbol points sk, 0, min and sk, 1, min from distances from the received signal point r as shown in FIG. 3, first. The two transmission symbol points are called reference points, and a pair of the reference points with their kth bits being 0 and 1 such as a pair of sk, 0, min and sk, 1, min is called a reference point pair. Next, as for each reference point of the reference point pair, the square of the distance between it and the received signal point r is calculated. After that, the square of the distance between sk, 0, min and r is subtracted from the square of the distance between sk, 1, min and r. Then the subtraction result is divided by 2σ2. The foregoing Expression (2) shows the computation. Actually, the computations are performed for each k to calculate an approximate value of the bit LLR for each of the eight bits constituting each symbol of the 256 QAM. The bit LLR of the kth bit calculated by the method of the Non-Patent Document 1 is designated as L1, k from now on.
In addition, Non-Patent Document 2 describes another bit LLR computation method. As shown in FIG. 4, in the configuration of the Non-Patent Document 2, an LLR computation device 200 receives feedback from an LDPC decoder 210 which is a post-stage of the LLR computation device 200. The LDPC decoder 210 carries out decoding of the LDPC code repeatedly using sum-product decoding, and feeds an intermediate decoding result (estimated bit string) obtained at each repeated stage back to the LLR computation device 200.
In the Non-Patent Document 2, the reference point pair is determined from the intermediate decoding result obtained by the configuration of FIG. 4. When designating the reference point pair by sk, 0, dec and sk, 1, dec, the LLR is calculated by Expression (3) which is an approximation of Expression (1). Incidentally, sk, 0, dec represents a transmission symbol point that has kth bit of 0 and has the other bits equal to the intermediate decoding result, and sk, 1, dec represents a transmission symbol point that has kth bit of 1 and has the other bits equal to the intermediate decoding result. FIG. 5 shows an example. As is clear from the comparison of Expression (3) with Expression (2), the Non-Patent Document 1 and the Non-Patent Document 2 has the same LLR computation method except for the determining method of the reference point pair. In the following, the bit LLR of the kth bit calculated by the method of the Non-Patent Document 2 is designated by L2, k.
                                                                        L                k                            =                            ⁢                                                ln                  ⁢                                                            ∑                                                                        s                          i                                                ∈                                                  C                                                      k                            ,                            0                                                                                                                ⁢                                          exp                      ⁡                                              (                                                  -                                                                                                                                                                                      r                                  -                                                                      s                                    i                                                                                                                                                              2                                                                                      2                              ⁢                                                              σ                                2                                                                                                                                    )                                                                                            -                                                                                                      ⁢                              ln                ⁢                                                      ∑                                                                  s                        i                                            ∈                                              C                                                  k                          ,                          1                                                                                                      ⁢                                      exp                    ⁡                                          (                                              -                                                                                                                                                                          r                                -                                                                  s                                  i                                                                                                                                                    2                                                                                2                            ⁢                                                          σ                              2                                                                                                                          )                                                                                                                                              ≈                            ⁢                                                ln                  ⁢                                                                          ⁢                                      exp                    ⁡                                          (                                              -                                                                                                                                                                          r                                -                                                                  s                                                                      k                                    ,                                    0                                    ,                                    dec                                                                                                                                                                                      2                                                                                2                            ⁢                                                          σ                              2                                                                                                                          )                                                                      -                                                                                                      ⁢                              ln                ⁢                                                                  ⁢                                  exp                  ⁡                                      (                                          -                                                                                                                                                              r                              -                                                              s                                                                  k                                  ,                                  1                                  ,                                  dec                                                                                                                                                                          2                                                                          2                          ⁢                                                      σ                            2                                                                                                                )                                                                                                                          =                            ⁢                                                                                          -                                                                                                                              r                            -                                                          s                                                              k                                ,                                0                                ,                                dec                                                                                                                                                              2                                                              +                                                                                                                    r                          -                                                      s                                                          k                              ,                              1                              ,                                                                                                                          ⁢                              dec                                                                                                                                                  2                                                                            2                    ⁢                                          σ                      2                                                                      :=                                  L                                      2                    ,                    k                                                                                                          (        3        )            